Verma Modules Over the Generalized Heisenberg–Virasoro Algebra

Abstract

For any additive subgroup G of an arbitrary field 𝔽 of characteristic zero, there corresponds a generalized Heisenberg–Virasoro algebra ℒ[G]. Given a total order of G compatible with its group structure, and any h, hI, c, cI, cLI ∈ 𝔽, a Verma module over ℒ[G] is defined. In this note, the irreducibility of Verma modules is completely determined.